The big idea: Efficiency = MA ÷ VR × 100%.
The velocity ratio is what the geometry promised; the mechanical advantage is what the machine actually delivered. The gap between them is friction, turned into heat — and it can also be written as useful energy out ÷ energy in.
MA and VR on the same mechanisms — and efficiency is the ratio between them.
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| System | Typical efficiency | Where the loss goes |
|---|---|---|
| Spur gear pair | About 96-99% per mesh | Sliding between tooth faces and churning the lubricant |
| Belt drive | About 95-98% | Belt flexing round the pulleys, plus a little creep and slip |
| Chain drive | About 97-98% | Friction at each pin and bush as every link articulates |
| Worm and wheel | Often only 40-70% | The thread SLIDES across the wheel teeth rather than rolling — which is also why it cannot be back-driven |
| Plain screw jack | Often below 40% | Deliberate: the friction is what stops the load winding itself back down |
Efficiencies multiply along a chain: Three stages at 95% each deliver 0.95 × 0.95 × 0.95 ≈ 86%, not 85% and certainly not 95%.
That compounding is the argument for removing a stage wherever one mechanism can do two jobs.
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Four ways to raise efficiency
Reduce friction at the contacts
Rolling bearings instead of plain holes, the right lubricant, smoother and harder bearing surfaces, and low-friction polymer bushes at pivots.
Stiffen the members
A handle or a shaft that flexes absorbs part of the movement into bending itself. Stiff members deliver the movement to the load instead.
Shorten the chain
Every extra stage multiplies in another loss and adds free play. Removing one stage is usually worth more than improving two.
Choose a rolling mechanism over a sliding one
Gears roll; a worm slides. That single difference is why one is above 95% and the other may be at 50%.
Sometimes low efficiency is the specification: A screw jack and a worm drive are inefficient on purpose: the friction is what holds the load when the operator lets go.
Making them efficient would let the car drop or the hoist run back. So a recommendation to reduce friction has to be checked against what the friction is doing.
How this is tested — calculating efficiency for gear- and belt-driven systems. It comes up two ways:
Paper 1 — multiple choice
- Calculate an efficiency from MA and VR.
- Find the overall efficiency of stages in series.
Paper 2 — analysing a product
- Calculate the efficiency of a described drive and comment.
- Explain how a designer could improve a mechanism's efficiency.
The trap: Recommending less friction without checking what it is for. A worm drive and a screw jack rely on friction to hold the load.
A hoist has a velocity ratio of 30 and lifts a 1,500 N load with a 75 N effort. Apply the formulae to find the MA and the efficiency, and comment on the value.
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